Biquadratic Exchange Coupling in Epitaxial Co$_{2}$MnSi/Cr/Fe Trilayers

Abstract

Interlayer exchange coupling (IEC) behavior in epitaxial Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> MnSi (20 nm)/Cr/Fe (7 nm) trilayers has been investigated against Cr spacer thickness (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cr</sub> = 0.3-6.3 nm). High-quality trilayer samples have grown on a Cr (5 nm)/Au (30 nm)/Cr (15 nm) buffer layer on a MgO substrate by ultrahigh vacuum (UHV) compatible dc sputtering method. A simple numerical simulation model has been used to explain magnetization process, which shows good agreement with the experimental M-H curves. The values of bilinear and biquadratic coupling energy (J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) and the cubic anisotropy energy of Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> MnSi and Fe (K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CMS</sub> and K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fe</sub> ) have been determined uniquely from the simulations. As a result, we have found a dominating contribution of biquadratic (90deg) coupling and absence of bilinear (180deg) coupling in all the samples with nonferromagnetic coupling. It has also been found that, the energetical competition between 90deg coupling energy and anisotropy energy largely affects the magnetization process due to different easy directions of bottom Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> MnSi (110) and Fe (100).